To describe and predict the vehicles′ two-dimensional movements under heterogeneous traffic environments (such as off-ramps)

this research firstly proposes the concept of virtual boundary field (VBF). The influence of VBF on driver behaviors is analyzed from a microscopic point of view. The VBF model hence is established. A two-dimensional IDM (intelligent driver model) model that considers the VBF is constructed which takes the surrounding vehicles into account. The proposed model is capable of describing and predicting the two-dimensional trajectories of vehicles. To calibrate the parameters in VBF

the dynamic time wrapping (DTW) is employed as the objective. The PSO (particle swarm optimization) is used to optimize the location of VBF. The validation results show that the trajectories prediction error is about 3.1%-8.2% for Mirror traffic data

and is 3.8%-28.2% for NGSIM data

and the proposed model is capable of describing and predicting the lateral and lateral two-dimensional motion of conventional vehicles in mixed traffic flow environments on ramps. The proposed model can be used to provide basic information for the trajectories planning of autonomous vehicles in mixed traffic flow.